Cambridge Lower Secondary Checkpoint

MATHEMATICS
1112/02
Paper 2
April 2020
1 hour
You must answer on the question paper.
You will need:
Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
 Answer all questions.
 Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
 Write your name, centre number and candidate number in the boxes at the top of the page.
 Write your answer to each question in the space provided.
 Do not use an erasable pen or correction fluid.
 Do not write on any bar codes.
 You should show all your working in the booklet.
 You may use a calculator.
INFORMATION
 The total mark for this paper is 50.
 The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages. Blank pages are indicated.
IB20 05_1112_02/6RP
© UCLES 2020
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2
1
Calculate the square root of 74
Give your answer correct to 1 decimal place.
[1]
2
Simplify these expressions.
f+f+f+f
2y + 6 – y + 1
[2]
3
Simplify fully this ratio.
12 : 30
:
4
[1]
Some trees are planted in rows of 10
Complete the formula to find the total number of trees, t, in r rows.
t=
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[1]
3
5
Chen rolls a dice and records the score each time.
The results are shown in the table.
Score
Frequency
1
9
2
14
3
2
4
12
5
8
6
5
Calculate his mean score.
[2]
6
10 cm
7 cm
7 cm
10 cm
NOT TO
SCALE
6 cm
Find the volume of the cuboid.
Give the units of your answer.
[2]
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4
7
Work out.
(1 + 2.5)2 – (1 + 2.52)
[1]
8
Here is a formula.
V = a(b – 5)2
Work out the value of V when a = 4 and b = 8
V=
9
[1]
Angelique travels 75 miles.
Jamila travels 115 kilometres.
Show that Angelique has travelled further than Jamila.
[1]
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5
10 Expand.
2a (2b – 3a)
[2]
11 Write the missing numbers in the boxes.
% of 250 = 75
75% of
= 300
[2]
12 These are the instructions on a box of grass seed.
1.5 kg of seed will cover
an area of 48 m2
Work out the amount of grass seed that is needed to cover an area of 256 m2.
kg [2]
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13 Round to two significant figures.
0.045 325
16 872
[2]
14 A circle has diameter 8 cm.
NOT TO
SCALE
8 cm
Calculate the circumference of the circle.
cm
[2]
15 Find the value of x.
93 × 9
= 9x
6
9
x =
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[1]
7
16 Here are some descriptions of how a variable y changes with time.
A The height ( y) of water in a bath as someone gets in and then after a few minutes gets
out and takes the plug out.
B The distance ( y) travelled by a runner who starts very fast and gradually slows down.
C The speed ( y) of a train which leaves a station, speeds up and then slows down to stop
again at the next station.
D The distance from home ( y) travelled by someone walking from home at a constant
speed to a shop and then, after shopping, walking home again at a constant speed.
E The speed ( y) of a cyclist who cycles slowly up a hill and then accelerates down the
other side.
For each graph, write the letter of the description that best describes its shape.
y
..............
y
..............
time
y
y
..............
time
..............
y
time
time
..............
time
[2]
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8
17 Factorise.
5b2  3b
[1]
18 The diagram shows a cuboid.
The length, width and height of the cuboid are all different.
Write down the number of planes of symmetry of this cuboid.
[1]
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9
19 D is directly proportional to T.
When T = 3, D = 36
(a) Find the formula connecting D and T.
[1]
(b) Find T when D is 66
[1]
(c) Draw the graph of the relationship between D and T for 0 ≤ T ≤ 10
D
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
T
[1]
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20 A quadrilateral is drawn on the grid below.
Show how the quadrilateral tessellates.
Draw 5 more of these quadrilaterals.
[1]
21 Here are the coordinates of five points.
Cross ( × ) the point that is not on the line with equation y = 5x – 3
(8, 37)
(2, 7)
(6, 27)
(5, 28)
(0, 3)
[1]
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11
22 The table shows the mean and range of the number of customers at a restaurant on
Mondays and Thursdays.
Mean
Range
Mondays
34
14
Thursdays
41
20
The restaurant manager says,
‘The number of customers on Mondays is less variable than on Thursdays.’
Explain why the manager is correct.
[1]
23 Convert 4 2 to a decimal.
7
Give your answer correct to 2 decimal places.
[1]
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24 The scale shows the mass of a van.
0
500
3500
3000
1000
kilograms
1500
2500
2000
Write down the mass of the van in tonnes.
tonnes
[1]
25 Find the nth term for this sequence.
3, 8, 13, 18, 23 …
[2]
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13
26 Here are some currency exchange rates.
1 US dollar = 7.76 HK dollars
1 US dollar = 1.47 NZ dollars
Work out the value of 1000 HK dollars in NZ dollars.
NZ dollars
[2]
27 A square and a regular hexagon are joined together along one edge.
NOT TO
SCALE
B
A
C
Find angle BAC.
°
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[2]
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28 Mia buys 50 coats at $28 each.
She sells 38 of these coats at $49 each.
She sells the rest of the coats at $40 each.
Find the overall percentage profit Mia has made on these coats.
%
[3]
29 Hassan travels by bus to work every morning.
The bus is either green or blue or yellow.
The table shows information about the probabilities of each colour.
Colour of bus
Probability
Green
Blue
Yellow
2x
2x
x
(a) Calculate the value of x.
x
[2]
(b) Work out the probability that Hassan’s bus is either blue or yellow.
[1]
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15
30 Find the inverse function of y = 3x
y=
[1]
31 ABCD is a square with side length 8 units.
The coordinates of D are ( p, q).
y
A
B
x
D
(p, q)
NOT TO
SCALE
C
The square is translated so that point B moves to point D.
Write down the coordinates of the new point A in terms of p and q.
(
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,
)
[2]
16
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© UCLES 2020
1112/02/A/M/20